If the distance from the moving point P to the x-axis is 2 less than the distance to the fixed point F (0,2), then the trajectory equation of the moving point is obtained

If the distance from the moving point P to the x-axis is 2 less than the distance to the fixed point F (0,2), then the trajectory equation of the moving point is obtained

The distance between the moving point P and the straight line y = - 2 is equal to the distance to the fixed point F (0,2)
So the trajectory of the moving point is a parabola
x²=8y

If the ratio of the distance from the moving point P to the X axis to the distance from the moving point P to the Y axis is 1 / 2, then the trajectory equation of the moving point P is?

It can be solved by direct method
Let P (x, y)
∵ the ratio of the distance from the moving point P to the x-axis to the distance from the moving point P to the y-axis is 1 / 2,
∴ |y|:|x|=1/2
∴ |y|=(1/2)|x|
Ψ y = (1 / 2) x or y = (- 1 / 2) x
Represents two straight lines